FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

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摘要 Let M be a closed n-manifold of positive sectional curvature. Assume that M admits an effective isometrical T1× Zpk-action with p prime. The main result of the article n＋1 for n 〉 5, then there exists a positive constant p（n）, is that ifk=lforn=3or k〉 n＋1/4 for n≥5,then there exists a positive constant p（n）,depending only on n, such that π1 （M） is cyclic if p ≥ p（n）. Let M be a closed n-manifold of positive sectional curvature. Assume that M admits an effective isometrical T1× Zpk-action with p prime. The main result of the article n＋1 for n 〉 5, then there exists a positive constant p（n）, is that ifk=lforn=3or k〉 n＋1/4 for n≥5,then there exists a positive constant p（n）,depending only on n, such that π1 （M） is cyclic if p ≥ p（n）.

作者王雨生

机构地区 School of Mathematical Sciences(& Laboratory of Mathematics and Complex Systems)

出处《Acta Mathematica Scientia》 SCIE CSCD 2010年第1期203-207,共5页 数学物理学报（B辑英文版）

基金 Supported partially by NSFC (10826052,10671018)

关键词 fundamental groups positive sectional curvature group actions fundamental groups positive sectional curvature group actions

分类号 O174.56 [理学—基础数学]

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2010年第1期

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FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

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